1) cats usually wont pee right in front of humans or cats, unless they believe you or the other cat is below them socially, cause marking your territory is picking a fight, this is also why they hide their poop too
2) Not all cats run away from an enemy they cant win, some cats will smack the enemy, then run (speaking from experience, poor dog didnt even realize what happened)
3) The reason why cats flee isnt because of such fear of others, they act like that because cats have little trouble finding food in most plaves. Thus, they have no reason to risk being injured to fight. Other larger cat species who have less food to work with are more aggressive